A Fourth Order Finite Difference Method for Singularly Perturbed Differential-Difference Equations

This paper deals with the singularly perturbed boundary value problem for a linear second order differential-difference equation of the convection-diffusion type with small delay parameter. A fourth order finite difference method is developed for solving singularly perturbed differential difference equations. To handle the delay argument, we construct a special type of mesh, so that the term containing delay lies on nodal points after discretization. The proposed finite difference method works nicely when the delay parameter is smaller or bigger to perturbation parameter. The truncation error of the finite difference method is calculated. On the basis of truncation error, as well as the results of number of computational examples, it is concluded that the present method offers significant advantage for the linear problems.